Dividing with Decimals Day 3

Big Idea:
How do you divide decimals by decimals? How can your estimation and number sense skills help you? Students work on answering these questions as they continue their work with dividing decimals.

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. A common mistake that students make when dividing with decimals is forgetting to put a zero in the quotient when the divisor cannot fit into that part of the dividend. Here, I want students to analyze the student’s work and explain their thinking. Students should be able to use their number sense to easily identify that the answer is correct. It may take students a little more time to determine what exactly went wrong. Students are engaging with MP3: Construct viable arguments and critique the reasoning of others. I ask the students what this student can do differently next time to prevent making a similar mistake. I want students to realize that making an estimate and checking your answer can prevent a lot of careless mistakes when dividing.

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I give students a few minutes to work on this problem independently. I want students to figure out a strategy for dividing decimals by decimals. I walk around to monitor student progress.

Some students may round the numbers and then make an estimate first. Others may use multiplication to guess and check how many hours Harold worked. Other students may try to divide with the decimal points, while others may ignore the decimal points until the end.

If a student is stuck, I may ask him/her the following questions:

Do you think he worked more or less than 5 hours? Why?

Do you think he worked more or less than 10 hours? Why?

What could you do to try to check?

I have 2-3 students share out their strategies and their thinking. I ask students if they made an estimate, and if so how they did it. I explain to students that this is our task today, to figure out a strategy that works of us to divide decimals by decimals.

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As mentioned in the do now, a common struggle with students is that they do not know where the decimal point should go in their quotient. We did a similar activity in the previous lesson (Dividing with Decimals Day 2), so students should be used to the structure. The difference is this time they will not be using calculators.

First, I give students a couple minutes to find the answer to 129 divided by 6. We review this answer. Next, students work with a partner to decide where the decimal point needs to go in the quotient. At first, students may complain or insist that they need to actually complete each division problem. I want students to use their number sense and estimation skills to figure it out. Students are engaging with MP7: Look for and make use of structure.

I ask students to share out strategies. How did you figure out where to put the decimal point in number 2? I want students to recognize that they are dividing a number that is close to 1 by 6, so the quotient has to be smaller than one. Some students may make the connection that 1 divided by 5 is the same as 1/5, which is equivalent to 0.2.

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I present the strategy of ignoring the decimal points until the end. I want students to use estimation and number sense skills to figure out where the decimal point goes. In the past I have tried to teach the procedure involving moving the decimal point the same number of times in the divisor and dividend and it has not worked with my students. It was just another over-complicated procedure that they forgot or misused.

I scaffolded these problems so that students are first just observing my work and then later doing the division for themselves. We talk through 1 and 2 together. I have students share out where they think the decimal point should go. We use multiplication to prove the answer works. For the “I know this because…” section I am looking for students to use a math fact to show their answer is reasonable. For number 1 a student may say “I know this because 0.5 x 10 = 5 and 0.5 x 20 = 10 and 0.5 x 30 = 20.”

I have students try number 3 on their own. I continue to stress the importance of using number sense and estimation skills to check and make sense of solutions. Students must use MP6: Attend to precision. I Post A Keyso that students can check their work when they finish a page. I am looking that students are making reasonable estimates and that they are successfully dividing using a strategy of their choice.

If many students are struggling we will come back together and work as a class. If fewer students are struggling, I may intervene in the following ways:

Ask them what their estimate is and how they got it.

Let them use a multiplication chart.

Give them a word problem situation that represents the problem.

Have them use the grids to organize their problems.

Pull a small group of students who are struggling to work together.

If students successfully complete the problems they can move on to the Challenge question about buying gas. If they need extra work they can also apply their decimal addition and subtraction skills with the Magic Square Decimals worksheet.

I begin the Closureby asking students to look at questions 5 and 6. What was your estimate? Why? How did you find the exact quotient? I look for students who used different strategies and I have them show and explain their work. If there is a common mistake I see students making, I will present it and ask students to address it here.

Brenda Ellis:
Your lessons are wonderful and very thorough. I thank you so much. I don't have the same time frame you have and I have to do small groups, but I am going to make this lesson work for me. I don't want to have to reteach whole groups of students when I don't have to, if they can get it from diligence the first time. Thank you so much for sharing. |
2 months ago |
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Jennifer Hixson:

Hi Andrea,

I really like your strategies on teaching multiplying and dividing with decimals. I'm wondering if you can explain a little more about leaving the decimals off when you divide. What do the students do when the decimal is repeating? How do they know when to stop if there's no decimal in the long division problem?